SQL Mathematical Operations Mastery

This challenge focuses on leveraging SQL's built-in mathematical functions to perform calculations and derive insights from data. Understanding these functions is crucial for data analysis, reporting, and building complex data-driven applications. You will be tasked with querying a database to compute various aggregate and scalar values using common mathematical operations.

Problem Description

Your goal is to write SQL queries that extract meaningful information by applying mathematical functions to data stored in a database table. This involves performing calculations such as rounding, absolute values, powers, and trigonometric operations.

Key Requirements:

• Query a provided table named measurements.
• Use SQL's standard mathematical functions to perform the required calculations.
• Return results in a clear, structured format.

Expected Behavior:

The queries should accurately compute the specified mathematical operations on the data within the measurements table. For each calculation, you will be asked to select the result along with a descriptive alias.

Edge Cases:

• Consider how functions handle NULL values.
• Be mindful of potential data type conversions and precision.
• Understand the behavior of functions with zero or negative inputs where applicable (e.g., SQRT).

Examples

Assume the following measurements table:

Example 1: Rounding a Value

Problem: Round the value to two decimal places for each record.

Input Table: measurements

Output:
| id  | rounded_value |
| :-- | :------------ |
| 1   | 12.35         |
| 2   | -9.88         |
| 3   | 5.00          |
| 4   | NULL          |
| 5   | 2.72          |

Explanation: The ROUND() function is used to round the value column to two decimal places. NULL values remain NULL.

Example 2: Calculating the Absolute Value

Problem: Calculate the absolute value of the value for each record.

Input Table: measurements

Output:
| id  | absolute_value |
| :-- | :------------- |
| 1   | 12.345         |
| 2   | 9.876          |
| 3   | 5.000          |
| 4   | NULL           |
| 5   | 2.71828        |

Explanation: The ABS() function is used to return the absolute (non-negative) value of the value column.

Example 3: Calculating a Power

Problem: Calculate the value raised to the power of 2 for each record.

Input Table: measurements

Output:
| id  | value_squared |
| :-- | :------------ |
| 1   | 152.399025    |
| 2   | 97.535376     |
| 3   | 25.000000     |
| 4   | NULL          |
| 5   | 7.38905609753984 |

Explanation: The POWER() function (or equivalent operator like ^ depending on SQL dialect) is used to calculate value to the power of 2.

Constraints

• The measurements table will contain at least one row.
• The id column is an integer and is unique.
• The value column is a numeric type (e.g., DECIMAL, FLOAT, REAL).
• Queries must be written in standard SQL syntax, compatible with most major database systems.
• Avoid using subqueries unless absolutely necessary for a specific complex mathematical transformation. Aim for direct application of functions.
• Performance should be reasonable for a table of up to 1,000,000 rows.

Notes

• SQL dialects may have slightly different function names or syntax for mathematical operations (e.g., ABS() vs. ABSOLUTE()). Use the most common or standard form.
• Pay attention to the return type of mathematical functions, especially when dealing with division or square roots, as it can affect precision.
• This challenge is designed to test your familiarity with common SQL mathematical functions like ROUND(), ABS(), POWER(), SQRT(), CEILING(), FLOOR(), TRUNCATE(), and trigonometric functions if applicable to specific sub-problems.